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Adaptive Sentencing Prediction with Guaranteed Accuracy and Legal Interpretability

Yifei Jin, Xin Zheng, Lei Guo

TL;DR

This paper tackles interpretable and accurate sentencing prediction under nonstationary data by introducing a Saturated Mechanistic Sentencing (SMS) model anchored in Chinese Criminal Law and an online Momentum LMS (MLMS) algorithm. It establishes theoretical bounds for adaptive prediction accuracy that do not rely on stationarity or independence, including a best-possible upper bound when parameters are known. The authors construct the Chinese Intentional Bodily Harm (CIBH) dataset with 82 feature factors and demonstrate that SMS-MLMS achieves high predictive accuracy, approaching the theoretical upper bounds and outperforming strong baselines. The work has practical implications for transparent judicial decision-making and offers a framework adaptable to other crimes and domains, supported by both Lyapunov/martingale analysis and real-world data validation.

Abstract

Existing research on judicial sentencing prediction predominantly relies on end-to-end models, which often neglect the inherent sentencing logic and lack interpretability-a critical requirement for both scholarly research and judicial practice. To address this challenge, we make three key contributions:First, we propose a novel Saturated Mechanistic Sentencing (SMS) model, which provides inherent legal interpretability by virtue of its foundation in China's Criminal Law. We also introduce the corresponding Momentum Least Mean Squares (MLMS) adaptive algorithm for this model. Second, for the MLMS algorithm based adaptive sentencing predictor, we establish a mathematical theory on the accuracy of adaptive prediction without resorting to any stationarity and independence assumptions on the data. We also provide a best possible upper bound for the prediction accuracy achievable by the best predictor designed in the known parameters case. Third, we construct a Chinese Intentional Bodily Harm (CIBH) dataset. Utilizing this real-world data, extensive experiments demonstrate that our approach achieves a prediction accuracy that is not far from the best possible theoretical upper bound, validating both the model's suitability and the algorithm's accuracy.

Adaptive Sentencing Prediction with Guaranteed Accuracy and Legal Interpretability

TL;DR

This paper tackles interpretable and accurate sentencing prediction under nonstationary data by introducing a Saturated Mechanistic Sentencing (SMS) model anchored in Chinese Criminal Law and an online Momentum LMS (MLMS) algorithm. It establishes theoretical bounds for adaptive prediction accuracy that do not rely on stationarity or independence, including a best-possible upper bound when parameters are known. The authors construct the Chinese Intentional Bodily Harm (CIBH) dataset with 82 feature factors and demonstrate that SMS-MLMS achieves high predictive accuracy, approaching the theoretical upper bounds and outperforming strong baselines. The work has practical implications for transparent judicial decision-making and offers a framework adaptable to other crimes and domains, supported by both Lyapunov/martingale analysis and real-world data validation.

Abstract

Existing research on judicial sentencing prediction predominantly relies on end-to-end models, which often neglect the inherent sentencing logic and lack interpretability-a critical requirement for both scholarly research and judicial practice. To address this challenge, we make three key contributions:First, we propose a novel Saturated Mechanistic Sentencing (SMS) model, which provides inherent legal interpretability by virtue of its foundation in China's Criminal Law. We also introduce the corresponding Momentum Least Mean Squares (MLMS) adaptive algorithm for this model. Second, for the MLMS algorithm based adaptive sentencing predictor, we establish a mathematical theory on the accuracy of adaptive prediction without resorting to any stationarity and independence assumptions on the data. We also provide a best possible upper bound for the prediction accuracy achievable by the best predictor designed in the known parameters case. Third, we construct a Chinese Intentional Bodily Harm (CIBH) dataset. Utilizing this real-world data, extensive experiments demonstrate that our approach achieves a prediction accuracy that is not far from the best possible theoretical upper bound, validating both the model's suitability and the algorithm's accuracy.

Paper Structure

This paper contains 17 sections, 8 theorems, 48 equations, 6 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Sentence Length Prediction
  3. Saturated Mechanistic Sentencing Model
  4. Algorithm Design
  5. Main Theorems
  6. Real-World Dataset Construction and Performance Evaluation
  7. Dataset Overview
  8. Validation of Theoretical Optimal Accuracy
  9. Effectiveness Evaluation
  10. Conclusion
  11. Proof of Main Theorems
  12. Dataset Construction
  13. Motivation
  14. Judgment Document Analysis
  15. Feature Extraction
  16. ...and 2 more sections

Key Result

Theorem 2.9

Under Assumptions A1--A3, we have the following lower bound to the accuracy of the adaptive predictor: where $\sigma_w^2 = \limsup\limits_{k\geq 0} \mathbb{E}[w_{k+1}^2 \mid \mathcal{F}_{k}]$, $w_{k+1}=y_{k+1}-G_k\left(\varphi_k^{\top} \theta_k\right)$ and $\mathcal{C}$ is a positive constant which does not dependent on $\sigma_w^2$ and $\xi$.

Figures (6)

  • Figure 1: Sentencing Process for Intentional Bodily Harm Cases
  • Figure 2: Extract features from different parts of the judgment document
  • Figure 3: minor variance
  • Figure 4: serious variance
  • Figure 5: Sentencing Factors for Intentional Bodily Harm Cases
  • ...and 1 more figures

Theorems & Definitions (19)

  • Remark 2.1
  • Remark 2.5
  • Definition 2.7
  • Remark 2.8
  • Theorem 2.9
  • Remark 2.10
  • Theorem 2.11
  • Lemma A.1
  • Lemma A.2
  • Lemma A.3
  • ...and 9 more